Subgroups — #49119320

Order 36224.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826870	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₂₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	#22583610	—	2	1	no	—
5	C₂×C₂₈₃⋊C₁₆	—	2	1	no	—
6	#22583544	—	2	1	no	—
7	#22583544	C₄	1	2	yes	—
8	C₄⋊C₈×C₂₈₃	—	2	1	no	—
9	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₆₆	—	4	1	no	—
11	C₄⋊Dic₂₈₃	—	2	2	no	—
12	C₄⋊Dic₂₈₃	—	4	1	no	—
13	C₂₈₃⋊C₁₆	—	4	1	no	—
14	C₂×C₈×C₂₈₃	—	4	1	no	—
15	C₂×C₈×C₂₈₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
17	C₄²×C₂₈₃	D₄	1	1	yes	characteristic
18	Dic₅₆₆	—	8	2	no	—
19	C₂×Dic₂₈₃	—	4	2	no	—
20	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₈₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₈₃	SD₁₆	1	1	yes	characteristic
23	C₈×C₂₈₃	—	2	1	no	—
24	C₈×C₂₈₃	—	8	1	no	—
25	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
26	C₈×C₂₈₃	Q₁₆	1	1	yes	characteristic
27	C₂²×C₂₈₃	#102	1	1	yes	characteristic
28	C₄×C₂₈₃	—	2	1	no	—
29	C₄×C₂₈₃	#101	1	1	yes	characteristic
30	C₄×C₂₈₃	#103	1	1	yes	characteristic
31	C₄×C₂₈₃	SD₃₂	1	1	yes	characteristic
32	C₄×C₂₈₃	Q₃₂	1	1	yes	characteristic
33	Dic₂₈₃	—	8	2	no	—
34	C₂×C₂₈₃	#332	1	1	yes	characteristic
35	C₂×C₂₈₃	#358	1	1	yes	characteristic
36	C₂×C₂₈₃	#361	1	1	yes	characteristic
37	C₂₈₃	#1365	1	1	yes	characteristic, complemented, Sylow
38	#1365	—	283	1	no	maximal, Sylow
39	#500	—	283	1	no	—
40	C₄⋊C₁₆	—	283	1	no	—
41	#335	D₂₈₃	1	1	yes	characteristic
42	C₄⋊Q₈	—	566	1	no	—
43	C₂×C₁₆	—	566	1	no	—
44	#107	—	283	2	no	—
45	#107	—	566	1	no	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
48	C₂×Q₈	—	1132	1	no	—
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₄×D₂₈₃	1	1	yes	characteristic
51	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
52	C₄⋊C₄	—	566	2	no	—
53	C₄⋊C₄	—	1132	1	no	—
54	C₄²	C₂²⋊D₂₈₃	1	1	yes	characteristic
55	C₁₆	—	1132	1	no	—
56	Q₈	—	2264	2	no	—
57	C₂×C₄	—	1132	2	no	—
58	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
59	C₂×C₄	#17985377	1	1	yes	characteristic
60	C₂×C₄	#17985379	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	#17985381	1	1	yes	characteristic
64	C₈	Dic₁₁₃₂	1	1	yes	characteristic
65	C₂²	#22583530	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	2264	2	no	—
68	C₄	#22583528	1	1	yes	characteristic
69	C₄	#22583535	1	1	yes	characteristic
70	C₄	#22583554	1	1	yes	characteristic
71	C₄	#22583556	1	1	yes	characteristic
72	C₂	#31826212	1	1	yes	characteristic
73	C₂	#31826268	1	1	yes	characteristic
74	C₂	#31826277	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22583530
commutator	C₂×C₈×C₂₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₃
Fitting	#335×C₂₈₃	C₂
socle, prime radical	C₂²×C₂₈₃	#102
cosocle	C₄×C₈×C₂₈₃	C₂²
hypercenter	#335	D₂₈₃
hypocenter	C₂₈₃	#1365
LCS	G ▷ C₂×C₈×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
37. C₂₈₃	#1365	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#31826870	2
C₄⋊(C₂₈₃⋊C₁₆)	2
#335×C₂₈₃	2
#1365	283